Notes I Basic concepts.pdf

7/28/2019 Notes I Basic concepts.pdf

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NM6605 Design and modelling of

Dr. Fan Wei Jun

- -.

Phone: 6790 4359

. .

School of EEE, NTU


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1. Semiconductor Fundamental

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Elemental

IIIA IVA VA VIA5 6 7

semiconductors

(e.g. Si - Silicon)

B C N

13 14 15 16

Al Si P SIIB

30 31 32 33 34

Ga Ge AsZn Se48 49 50 51 52

In Sn SbCd Te

80

Hg ompoun sem con uc ors(e.g. III-V: GaAs, InP, GaN,

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, , , .


6/20

Si is the diamond structure

sublattices, offset from one

.

a body diagonal.

Zinc blende structure: the two offset lattices are of different atoms.Each group III site is surrounded by 4 group V sites, and vice-versa.

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7/20

The semiconductor is said to be indirect when the conduction band

m n mum an va ence an max mum o no co nc e e.g. e, , s,

AlP, AlSb, GaP). Example: Band diagram for Si - indirect (Eg=1.12 eV)Energy (E)

on uc on an

k[100]k[111]

bandgap

valence bandheavyholes

light holes

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8/20

In a direct bandgap material, the conduction band minimum andrec an gap

valence band maximum coincide in k-space (e.g. GaAs, GaSb, InP,

InAs, InSb, GaN) Example: Band diagram for GaAs (Eg = 1.42 eV) k is specified in two different

crystallographic directions.

Energy (E)

conduction bandMinima referred to as , L and X

points

Two t es of holes exist with

XL

different effective masses -

heavy holes and light holes.

bandgapEgL Eg

EgX

ect ve mass s re ate to t e

E-k curvature.

Why GaN is transparent, GaAs not?valence band

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9/20

r t ca po nts n t e rst r ou n zone o a z nc en e sem con uctor

(0, 0, 0)

L (0.5, 0.5, 0.5)

, ,U,K (0.25,0.25,1)

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10/20

Band structure including spin-orbit interaction

One re evant con uct on an s

formed from S- like atomic orbitals

(wavefunction is approximately

spherically symmetric)

three u er valence bands formed

from (three) P- like orbitals

-

lowest, split-off hole (i. e., valence)

band remaining two hole bands have

zone center heavy hole (hh) band,

and the other is the light hole (lh)

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an


11/20

Band diagram for GaAs

In a direct semiconductor, we

-

at the centre of the Brillouin zone.Energy (E)

*2 egC

m

kEE

*2 h

Vm

kE

If the interactions with the latticeare taken into account - so we

XL

introduce an effective mass

12

k[100]k[111]

2

2*

dk

me valence band

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12/20

If the lattice constant of the e itaxial la er a is different from that

Lattice matching and strain

of the substrate (as), defects in the crystal structure can occur.

Misfit

isolated combined

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att ces att ces


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For perfect epitaxial growth af=as, there is no mismatch, so the

epi-layer is unstrained

However, a small mismatch can be accepted, causing an elasticallystrained layer, but the layer must be thin for defects not to occur.

Strained

z (growthdirection)

isolatedcombined

latticesx

y

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lattices


14/20

Lattice matching and strain

-

=//= xx = yy = (as-af)/ af

s , -layer lattice constant without strain.

<

// >0 Tensile strain

r i l r in

= zz = - 2(C12/C11)//

h r 11 n 12 r l i iffn n n Formost of the III-V semiconductors, C12 0.5 C11.

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15/20

Strain energy - will accumulate

and is linear with thickness. A

critical thickness occurs at whichstrain energy is higher than

dislocation energy - defects occur.

This happens at the criticalthickness: dc as / |2| . Accurate

calculation should use Matthews

equation.Substrate layer is many times thicker than the epitaxial layer. Defects are

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.


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ra n n uence on an structure

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17/20

ue to y rostat c stra n, t e con uct on an e ge sshifted by

c = ac xx +yy +zz = ac - 12 11

and the valence band edge is shifted byP

= - av(xx +yy +zz ) = -2av(1-C12/C11)

So the bandgap after hydrostatic strain is

Egs = Eg + Ec + P= E + 2 a -a 1-C /C

Due to shear strain, the heavy hole is shifted by

= - - = - xx yy zz 12 11

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18/20

Band lineup

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19/20

Band offset calculation

EV = Evav + /3

EcEc=Ec(B)-Ec(A)

cEvEg=Ec-Ev

v

Evav/3

v=- V - V

A Bvav

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20/20

uan um we n rare p o o e ec or QWIPs operate by photoexcitation of electrons between ground and

rst exc te state su an s o mu t -quantum we s s . n er

applied bias, the photo-excited carriers can escape from the potential

.

The lattice matched

x 1-x

system is commonly used tocreate a QWIP structure. Thelight detection can be at anywavelength range between 6-20

*

22

*

222

* 22)(

2

1),,(

m

k

m

k

W

n

mkknEE

yxyx

School of EEE, NTU

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Notes I Basic concepts.pdf